Differential forms, Fukaya A∞A_\infty algebras, and Gromov-Witten axioms

Consider the differential forms $A^*(L)$ on a Lagrangian submanifold $L \subset X$. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved $A_\infty$ structures on $A^*(L),$ parameterized by the cohomology of $X$ relative to $L.$ The family of $A_\infty$ structures satisfies properties analogous to the axioms of Gromov-Witten theory. Our construction is canonical up to $A_\infty$ pseudoisotopy. We work in the situation that moduli spaces are regular and boundary evaluation maps are submersions, and thus we do not use the theory of the virtual fundamental class.Comment: 51 pages, 6 figures; improved exposition, added illustrations, corrected minor errors, added reference

Incorporating Social Media into the Classroom: A Case Study on How TikTok can be Immersed into Classroom Pedagogy

My research project focuses on the use of TikTok embedded within classroom pedagogy and how it can be used as a tool to support academic and social emotional wellbeing. There is a lack of research investigating how social media can be incorporated into the classroom to make up for potential academic losses, including the inevitable social/emotional needs of adolescents that need to be addressed due to the ramifications of COVID-19. In my research, I question ways in which students see this tool as supporting their wellbeing, in what ways parents see this tool as supporting their child\u27s wellbeing, and why TikTok is unique to successfully building a community. This project offers valuable insights into Generation Z on a deeper social-emotional level through fieldwork observation notes, surveys, and interviews with students and parents. My findings show that social media and classroom curriculum can work in tandem as a tool to increase engagement and support social emotional wellbeing and academic success. The TikTok application requires demonstrating 21st century skills, enhances social relationships, and builds a connected classroom community. Finally, this project’s findings demonstrate how educators can support the whole child through using tools such as TikTok to help provide social emotional support for highly anxious students. In the words of one participant, TikTok “makes everyone feel like they belong.

Relative quantum cohomology

We establish a system of PDE, called open WDVV, that constrains the bulk-deformed superpotential and associated open Gromov-Witten invariants of a Lagrangian submanifold $L \subset X$ with a bounding chain. Simultaneously, we define the quantum cohomology algebra of $X$ relative to $L$ and prove its associativity. We also define the relative quantum connection and prove it is flat. A wall-crossing formula is derived that allows the interchange of point-like boundary constraints and certain interior constraints in open Gromov-Witten invariants. Another result is a vanishing theorem for open Gromov-Witten invariants of homologically non-trivial Lagrangians with more than one point-like boundary constraint. In this case, the open Gromov-Witten invariants with one point-like boundary constraint are shown to recover certain closed invariants. From open WDVV and the wall-crossing formula, a system of recursive relations is derived that entirely determines the open Gromov-Witten invariants of $(X,L) = (\mathbb{C}P^n, \mathbb{R}P^n)$ with $n$ odd, defined in previous work of the authors. Thus, we obtain explicit formulas for enumerative invariants defined using the Fukaya-Oh-Ohta-Ono theory of bounding chains.Comment: 69 pages, 6 figures; corrected minor errors, improved expositio

Precision Prevention and Public Health

A new trend, “Precision Prevention,” is emerging in public health. This term is borrowed from “Precision Medicine,” a concept in medicine that allows for individualized treatments for patients. Precision prevention utilizes “biologic, behavioral, socioeconomic, and epidemiologic data to devise and implement strategies” tailored to specific individuals or populations. The goal of precision prevention is to target the “right intervention to the right population at the right time.” Much of precision prevention accounts for one’s social determinants of health, tailoring interventions based on a set of individual factors related to where we live, learn, work, and play that impact our health. Precision prevention works to move away from universal approaches to illness and injury prevention. Flaura Koplin Winston, MD, MPH, Chair of the Science and Medical Advisory Committee for Entrepreneurship and Innovation at The Children’s Hospital of Philadelphia (CHOP), applies a precision prevention framework, using a “tiered risk model” (see figure 1) for the Violence Prevention Initiative at CHOP. In the tiered risk model, there are three types of interventions focused around the needs of universal, selected, and indicated populations. At each level, interventions range from meeting the universal needs of the general population, to the select needs of populations at increased or different risk, and finally to interventions tailored for populations with adverse or indicated needs. For example, within the Violence Prevention Initiative, selected interventions that integrate appropriate community support services are tailored to children at greater risk for violence, and indicated interventions tailor the most intensive, direct support to child victims of violence.https://repository.upenn.edu/publichealth_databriefs/1001/thumbnail.jp

Characteristics of Persons With Severe Mental Illness Who Have Been Incarcerated for Murder

In this descriptive study, we analyzed data collected from multiple state agencies on 95 persons with severe mental illness who were convicted of murder in Indiana between 1990 and 2002. Subjects were predominately suffering from a mood disorder, were white and male with a high school education or equivalent, were living in stabilized housing, and, to a lesser degree, were involved in significant intimate and familial relationships. Rage or anger, overwhelmingly directed toward intimate or familial relations by the use of a firearm or sharp object, was the most frequently mentioned motive for murder. Most of those studied had been raised in households with significant family dysfunction, had extensive histories of substance abuse and criminality, and had received little treatment for their mental and substance use disorders. Findings are contextualized and compared with similarly descriptive studies of nonlethal violence and persons with a mental illness; hospitalized, schizophrenic and psychotic murderers; and homicide offenders outside the United States

The Opioid Crisis

Opioid use and addiction have reached epidemic proportions in Philadelphia, making drug overdose involving opioids a leading cause of death. Both pharmaceutical and illicit opioids contribute to this crisis. Opioid sales in Philadelphia more than doubled between 2000 and 2012, and health care providers continue to prescribe opioid pain medication in greater quantities than medically appropriate. The peak age group for overdoses is 45-54, an older age group than previously seen. Over-prescribing of opioids contributes to the recruitment of adults into drug dependence. While use of opioid pain medications usually does not lead to opioid use disorder, four out of five heroin users nationwide transitioned from original use of prescription medications. Heroin is easy to obtain, potent and cheap compared to prescription pain medications. There are estimated to be at least 70,000 heroin users in Philadelphia.https://repository.upenn.edu/publichealth_databriefs/1003/thumbnail.jp

Advances in Digital Health Research

Social media and emerging mobile technologies have sparked radical shifts in human behavior, with people worldwide spending an average of 2 hours and 15 minutes daily on social networks. Facebook, Instagram, and Twitter have more than 2 billion users globally. Social networking site use has risen dramatically by all age groups, with the highest use among 18-29 year olds (see Figure below). Every second, Twitter users send 6,000 tweets, amounting to 500 million tweets per day. Instagram users post approximately 95 million photos, generating 4.2 billion likes, each day. A newer platform, Snapchat, has 178 million daily users, 60% of whom are under 25 years of age. They share an average of 3 billion snaps, or rapidly vanishing photos, every day. Researchers at Penn are turning these Tweets, posts, and snaps into innovative data sources that hold vital clues about behaviors, emotions, preferences, opinions, and social networks—all with potential implications for population health. Through the analysis of keywords, images, phrases, emoticons, likes, and hashtags, Penn teams are turning troves of digital information into human-centered health interventions and educational initiatives.https://repository.upenn.edu/publichealth_databriefs/1004/thumbnail.jp

Examining the impact of comorbid serious mental illness on rehospitalization among medical and surgical inpatients

Multiple barriers to quality health care may affect the outcomes of postacute treatment for individuals with serious mental illness (SMI). This study examined rehospitalization for medical and surgical inpatients with and without a comorbid diagnosis of SMI which included psychotic disorders, bipolar disorder and major depressio

Examining the impact of comorbid serious mental illness on rehospitalization among medical and surgical inpatients

Multiple barriers to quality health care may affect the outcomes of postacute treatment for individuals with serious mental illness (SMI). This study examined rehospitalization for medical and surgical inpatients with and without a comorbid diagnosis of SMI which included psychotic disorders, bipolar disorder and major depressio